Geodesic
Elementary quotient completion
Theory and applications of categories, CT2011, Tome 27 (2012), pp. 445-463

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We extend the notion of exact completion on a category with weak finite limits to Lawvere's elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which is the universal solution to adding certain quotients. We note that the elementary quotient completion can be obtained as the composite of two other universal constructions: one adds effective quotients, the other forces extensionality of morphisms. We also prove that each construction preserves comprehension.

Publié le :
Classification : 03G30 03B15 18C50 03B20 03F55
Keywords: quotient completion, split fibration, universal construction 
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     author = {Maria Emilia Maietti and Giuseppe Rosolini},
     title = {Elementary quotient completion},
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     volume = {27},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2012_27_a16/}
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Maria Emilia Maietti; Giuseppe Rosolini. Elementary quotient completion. Theory and applications of categories, CT2011, Tome 27 (2012), pp. 445-463. http://geodesic.mathdoc.fr/item/TAC_2012_27_a16/